A199879 Continued fraction for x value of the unique pairwise intersection on (0,1) of distinct order 5 power tower functions with parentheses inserted.

0, 2, 2, 1, 35, 1, 2, 2, 1, 2, 5, 3, 1, 1, 45, 1, 1, 6, 11, 2, 9, 2, 2, 2, 2, 1, 1, 1, 29, 1, 3, 7, 4, 1, 7, 61, 1, 1, 2, 1, 2, 6, 2, 1, 1, 96, 11, 1, 2, 1, 1, 4, 14, 1, 10, 1, 2, 1, 7, 4, 7, 5, 10, 1, 6, 2, 2, 9, 6, 8, 3, 1, 3, 1, 3, 7, 9

Offset

1,2

Links

Table of n, a(n) for n=1..77.

Example

0.42801103796472992390204...

Maple

with(numtheory):
f:= x-> (x^(x^x))^(x^x): g:= x-> x^(x^((x^x)^x)):
Digits:= 200:
xv:= fsolve(f(x)=g(x), x=0..0.99):
cfrac(evalf(xv), 120, 'quotients')[];

Mathematica

terms = 77; digits = terms+10; xv = x /. FindRoot[x^(x^2) - 2x == 0, {x, 1/2}, WorkingPrecision -> digits]; ContinuedFraction[xv, terms] (* Jean-François Alcover, Mar 24 2017 *)

Crossrefs

Cf. A199814 (decimal expansion), A199880 (Engel expansion).

Sequence in context: A048660 A019227 A163893 * A006828 A091752 A078078

Adjacent sequences: A199876 A199877 A199878 * A199880 A199881 A199882

Keyword

nonn,cofr

Author

Alois P. Heinz, Nov 11 2011

Status

approved